1. Field of the Invention
The present invention relates to an X-ray imaging system and method for nondestructive testing of the inside of an object.
2. Description of the Related Art
Imaging systems for nondestructive observation of the inside of a sample using X-rays include an absorption-contrast X-ray imaging system using a change in X-ray intensity caused by the sample as image contrast, and a phase-contrast X-ray imaging system using a change in phase as the contrast. The former, namely, the absorption-contrast X-ray imaging system, is mainly composed of an X-ray source, a sample setting mechanism and a detector. The X-rays emitted from the X-ray source are irradiated on the sample positioned by the sample placement mechanism, and the X-rays that have passed through the sample are detected by the detector. Thereby, an image using the change in the intensity of X-rays caused by the sample absorption as the contrast is obtained. Because of a simple principle of measurement and a simple system configuration, this system is widely used in many fields including medical diagnosis, in the name of roentgen for two-dimensional observation and X-ray computed tomography (CT) for three-dimensional observation.
On the other hand, the latter, namely, the phase-contrast X-ray imaging system, requires a means for detecting a phase-shift to the above-mentioned system configuration in addition; however, this system is capable of observing biological soft tissues, with extremely high sensitivity, without contrast agents and with low X-ray damage, as compared to the absorption-contrast X-ray imaging system. This is due to the fact that a scattering cross-section that effects the phase-shift is, in terms of light elements, about 1000 times larger than a scattering cross-section that effects the change in the intensity. The phase-shift detecting means include (1) a method using an X-ray interferometer (i.e., an X-ray interference method), as disclosed in Japanese Unexamined Patent Application Publication No. Hei 4-348262; (2) a method utilizing a refraction angle θ of the X-rays which is proportional to spatial differential of the phase-shift (i.e., a refraction-contrast method, diffraction enhanced imaging (DEI)), as disclosed in Japanese Patent Application Publication No. Hei 9-187455; and (3) a method using X-ray Fresnel diffraction. The difference in principle among the above-mentioned methods is that the method (1), namely, the X-ray interference method, is detecting the phase-shift directly, whereas the other methods are detecting the spatial differential of the phase-shift. Description will be outlined below with regard to the methods (1) and (2) concerned deeply with the present invention.
The system for the above-mentioned method (1), namely, the X-ray interference method, is composed of the X-ray interferometer, such as a Bonse-Hart interferometer (such as described in Appl. Phys. Lett. 6, 155 (1965)) or an interferometer by dividing the crystal of this type of interferometer into multiple crystal blocks (such as described in J. Appl. Cryst. 7, 593 (1974)), in addition to the X-ray source, the sample placement mechanism and the detector.
FIG. 1 is a perspective view schematically showing the configuration of the Bonse-Hart interferometer. The Bonse-Hart interferometer includes three wafers (a beam splitter 1, a mirror 2, and an analyzer 3) disposed parallel to one another at regular intervals, and is made of a crystal block formed monolithically of a single crystal ingot. An incident X-ray 4 is split by the first wafer (the beam splitter 1) into two beams 5 and 6, which are thereafter reflected by the second wafer (the mirror 2) and then combined at the third wafer (the analyzer 3) to form two interference beams 7 and 8. When a sample 9 is installed on an optical path of any one of the split beams 5 and 6, a phase-shift p of the beams caused by the sample 9 changes the intensity of the interference beams 7 and 8 by superposition (or interference) of waves. Utilizing this principle, an image (or a phase-map) indicating spatial distribution of the phase-shift p caused by the sample is obtained, by using a method called “sub-fringe”, from an intensity distribution image of the interference beams 7 and 8 detected by an image detector or the like. In this instance, using, as the sub-fringe method, a Fourier transform method disclosed in Appl. Opt. 13 (1974) 2693 enables to obtain the phase-map from a single interference image and thus to observe even a phenomenon that changes rapidly with time. Also, imaging systems capable of three-dimensional nondestructive observation using a combination of the phase-contrast imaging method and a typical X-ray CT approach include the system disclosed in Japanese Unexamined Patent Application Publication No. Hei 4-348262. As in the case of the typical X-ray CT, this system involves irradiating a sample with X-rays in multiple different directions, and reconstructs a cross-section image of the sample by computation based on a phase-map acquired for each projection.
The above DEI method (2) obtains the phase shift p, utilizing a phenomenon in which the direction of propagation (or a wavefront) of the X-ray is slightly diverged by refraction as shown in FIG. 2 if the phase shift p is spatially nonuniform when the X-ray passes through a sample that causes the phase shift p. The refraction angle θ of the X-ray caused by the sample is given by Equation (1) as a function of the spatial differential of p:
                    θ        =                              λ                          2              ⁢                                                          ⁢              π                                ⁢                                    ⅆ              p                                      ⅆ              x                                                          (        1        )            where λ denotes the wavelength of the X-ray. Thus, detection of θ enables to obtain the spatial differential of the phase shift p, and further, the spatial integration enables to obtain the phase shift p.
In a hard X-ray region, the refraction angle θ is generally a very small value of approximately a few μrad. Thus, X-ray diffraction of a flat plate single crystal 10 called an analyzer crystal is utilized for detection of θ (see FIG. 2). When an incident angle θB of the X-ray with respect to the analyzer crystal satisfies diffraction conditions expressed as the following Equation (2):λ=2d sin θB  (2)within a range of angles of a few grad, the incident X-ray is diffracted (or reflected) by the analyzer crystal. Here, d denotes a lattice spacing of diffraction plane. Accordingly, when the direction of propagation of the X-ray is not diverged (θ=0), the incident angle of the X-ray with respect to the analyzer crystal is set so as to satisfy Equation (2), and thereby, intensity I of the diffracted X-ray depends on θ and gets the maximum when θ=0, and decreases with increasing of θ and gets almost zero when θ equals a few μrad. Utilizing this phenomenon, θ, that is, an image, the contrast of which is represented by the amount of spatial differential of the phase-shift, can be obtained from the spatial distribution (or the diffraction image) of the diffraction intensity I, and further, an image (or the phase map) showing the spatial distribution of the phase shift p can be obtained by integration calculation. Incidentally, besides X-ray diffraction based on Bragg-case, a method utilizing X-ray diffraction based on X-ray transmission Laue-case is also developed (see Jpn. J. Appl. Phys. 40 (2001) L844), and recently, a method utilizing a transmitted wave is called a dark field, and a method utilizing a diffracted wave is called a bright field.
As can be seen from FIG. 2, the use of a single diffracted image (or reflected image) alone cannot distinguish between the change in intensity caused by the absorption of the X-ray by the sample and the change in intensity caused by θ, and hence cannot quantitatively determine θ. Thus, generally, the DEI method involves rotating the analyzer crystal in the vicinity of a Bragg angle, and calculating θ from multiple obtained diffracted images. In this instance, rotation methods include (a) a “two-point method” using two angles alone for measurement (see Phys. Med. Biol. 42 (1997) 2015), and (b) a “scan method” using three or more angles for measurement (see Japanese Patent Application Publication No. Hei 9-187455).
The “two-point method” (a) uses two angles which sandwich a Bragg angle θB to obtain an image. If the incident angle of the X-ray on the analyzer crystal is set to an angle at which the diffraction intensity value is half of the peak value (θB±dθD/2), intensity Ir of the X-ray diffracted by the crystal is given by Equation (3):
                              I          r                =                              I            o                    ⁢                      R            ⁡                          (                                                                    θ                    B                                    ±                                                            d                      ⁢                                                                                          ⁢                                              θ                        D                                                              2                                                  +                θ                            )                                                          (        3        )            where Io denotes intensity of the incident X-ray, and R denotes reflectance of the analyzer crystal. At the above angle, R is substantially proportional to θ, so that R can be approximated by a second-order Taylor expansion as given by Equation (4).
                              R          ⁡                      (                                                            θ                  B                                ±                                                      d                    ⁢                                                                                  ⁢                                          θ                      D                                                        2                                            +              θ                        )                          =                              R            ⁡                          (                                                                    θ                    B                                    ±                                                            d                      ⁢                                                                                          ⁢                                              θ                        D                                                              2                                                  +                θ                            )                                +                                                    ⅆ                R                                            ⅆ                θ                                      ⁢            θ                                              (        4        )            
The diffraction intensity (I1 and Ih) at a low angle (θL=θB−dθD/2) and a high angle (θH=θB+dθD/2) are expressed as Equations (5) and (6), respectively, from Equations (3) and (4).
                              I          l                =                              I            o                    ⁡                      (                                          R                ⁡                                  (                                      θ                    L                                    )                                            +                                                                    ⅆ                    R                                                        ⅆ                    θ                                                  ⁢                θ                                      )                                              (        5        )                                          I          h                =                              I            o                    ⁡                      (                                          R                ⁡                                  (                                      θ                    H                                    )                                            +                                                                    ⅆ                    R                                                        ⅆ                    θ                                                  ⁢                θ                                      )                                              (        6        )            
Erasing I0 from the above equations leads finally to θ being expressed as Equation (7).
                    θ        =                                                            I                l                            ⁢                              R                ⁡                                  (                                      θ                    L                                    )                                                      -                                          I                h                            ⁢                              R                ⁡                                  (                                      θ                    H                                    )                                                                                                        I                l                            ⁢                                                ⅆ                  R                                                  ⅆ                  θ                                            ⁢                              (                                  θ                  H                                )                                      -                                          I                h                            ⁢                                                ⅆ                  R                                                  ⅆ                  θ                                            ⁢                              (                                  θ                  L                                )                                                                        (        7        )            
Accordingly, the refraction angle θ (x, y) at each point (or pixel) on the sample can be obtained by performing calculation of Equation (7) for each point of I1 and Ih obtained at the above two angles. Also, the phase-map can be obtained by integrating θ (x, y) at each obtained point in a direction horizontal to the sheet of FIG. 3. Note that, if there is a great change in density of the sample and thus a change in θ is greater than an angular width of diffraction (up to dθD), the diffraction intensity becomes zero or a value different from the intended value over the diffraction peak, and cannot be detected normally. Thus, the largest dp/dx value detectable with this method is limited by Equation (8).
                                          ⅆ            p                                ⅆ            x                          =                                            d              ⁢                                                          ⁢                              θ                D                                      2                    ⁢                                    2              ⁢              π                        λ                                              (        8        )            
The “scan method” (b) involves, as shown in FIG. 4, rotating the analyzer crystal at an angle of the angular width of diffraction (up to dθD) or greater in the vicinity of the Bragg angle, and calculating the refraction angle θ from multiple obtained diffracted images (typically, three or more images). This method is characterized in that rotation of the analyzer crystal at a large angle enables detection of θ greater than dθD/2, and there is no limitation on a density dynamic range, which is a problem of the method (a).
In this method, the diffraction intensity changes as shown in FIG. 5 with the rotation θA of the analyzer crystal, and thus, the intensity of the diffracted beam of the X-ray that passed through each point (x, y) on the sample has a peak at an angle offset by the refraction angle θ from the Bragg angle θB. Thus, the refraction angle θ can be calculated from Equation (9) as the center of the intensity of the diffracted beam:
                              θ          ⁡                      (                          x              ,              y                        )                          =                                            ∑              n                        ⁢                                                  ⁢                                          θ                n                            ⁢                                                I                  n                                ⁡                                  (                                                            θ                      n                                        ,                    x                    ,                    y                                    )                                                                                        ∑              n                        ⁢                                                  ⁢                                          I                n                            ⁡                              (                                                      θ                    n                                    ,                  x                  ,                  y                                )                                                                        (        9        )            where θn denotes each angle of the analyzer crystal, and In(θn) denotes the intensity of the diffracted beam obtained at θn. Thus, the spatial distribution image (or the phase-map) of the phase shift p can be obtained by integrating θ (x, y) at each obtained point in a direction horizontal to the sheet of FIG. 4, as in the case of the two-point method.
Also, the DEI method can involve rotating the sample with respect to the incident X-ray and nondestructively obtaining the cross-section image of the sample by calculation of reconstruction from the projection image obtained at each angle, as in the existing X-ray CT.